Riemann’s Boundary Value Problem of K-Analytic Functions
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摘要: 引入了(分片)K-解析函数和Cauchy型K-积分的概念.利用K-对称变换的方法研究了Cauchy型K-积分的某些性质,然后借助函数在曲线上的指标与这些Cauchy型K-积分的性质,得到了K-解析函数类中的Riemann边值问题的可解条件和解的表达式以及它们与指标之间的关系.而解析函数和共轭解析函数都是K-解析函数的特例,文中所得结果,推广了解析函数和共轭解析函数中的相应结论.
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关键词:
- Cauchy型K-积分 /
- (分片)K-解析函数 /
- K-对称变换 /
- 边界值公式 /
- Riemann边值问题 /
- 指标
Abstract: First, the concepts of the (piecewise) K-analytic function and the Cauchy type K-integral were introduced, and some properties of the Cauchy type K-integral were studied through K-symmetry transformation. Then, with the function index of the curve and the properties of the Cauchy type K-integral, the solvable conditions and the solution expressions for the Riemann’s boundary value problem of the K-analytic function as well as the relationship between the solutions and the index were obtained. Since both the analytic functions and the conjugate analytic functions are special cases of the K-analytic functions, the present conclusions generalize many known related results of them. -
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